Intersection-free uniform set family
= Intersection-free uniform set family
An <intersection-free uniform set family> is a <uniform set family> $\mathcal F$ with no three distinct members $A,B,C$ satisfying $A\cap B\subseteq C$. For distinct members of a rank-$r$ family, $|A\cap B|<r$, so using strict containment gives the same restriction. Fixing one member turns the other members' intersections with it into distinct <antichain> traces, giving the <antichain trace bound for intersection-free families>.